Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open instances could be solved to optimality.     

Effect of non-associated electrolyte solutions on the behaviour of poly(vinyl alcohol)-based hydrogels

The aim of this paper is to present the behaviour of the poly(vinyl alcohol) hydrogels [PVA-HG] in sodium and potassium chlorides aqueous solutions, due to their interactions. The tested [PVA-HG]-s have been obtained by repeated freezing and thawing cycles. White, heterogeneous hydrogels have been obtained. These hydrogels exhibit a mechanical active behaviour at their contact with electrolytes aqueous solutions, manifested by important changing in mass, volume and density of the hydrogel samples. These modifications could be explained by water elimination from the hydrogels that initially reached the equilibrium of swelling. The kinetic of the water desorption and the reversibility of this process, have been studied and some of the factors that influence this behaviour have been evidenced. The sensitivity of PVA hydrogels to electrolyte nature and concentration could be used in sensors design and also could explain some aspects of electrolytes diffusion through PVA membranes and targeted drugs delivery.     

A formula with some applications to the theory of Lyapunov exponents

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products. Financial support from Pronex-Dynamical Systems, CNP_q 001/2000 and from Faperj is gratefully acknowledged.     

Banach envelopes of vector valued H spaces

In the paper we describe the Banach envelopes of Hardy spaces of analytic functions of several variables on polydiscs taking values in quasi-Banach spaces.     

Guest‐Induced Transformation of a Porphyrin‐Edged FeII4L6 Capsule into a CuIFeII2L4 Fullerene Receptor

The combination of a bent diamino(nickel(II) porphyrin) with 2‐formylpyridine and Fe^II yielded an Fe^II₄L₆ cage. Upon treatment with the fullerenes C₆₀ or C₇₀, this cage was found to transform into a new host–guest complex incorporating three Fe^II centers and four porphyrin ligands, in an arrangement that is hypothesized to maximize π interactions between the porphyrin units of the host and the fullerene guest bound within its central cavity. The new complex shows coordinative unsaturation at one of the Fe^II centers as the result of the incommensurate metal‐to‐ligand ratio, which enabled the preparation of a heterometallic cone‐shaped Cu^IFe^II₂L₄ adduct of C₆₀ or C₇₀.     

Controlled Light‐Mediated Preparation of Gold Nanoparticles by a Norrish Type I Reaction of Photoactive Polymers

Gold nanoparticles (AuNPs) are subjects of broad interest in scientific community due to their promising physicochemical properties. Herein we report the facile and controlled light‐mediated preparation of gold nanoparticles through a Norrish type I reaction of photoactive polymers. These carefully designed polymers act as reagents for the photochemical reduction of gold ions, as well as stabilizers for the in situ generated AuNPs. Manipulating the length and composition of the photoactive polymers allows for control of AuNP size. Nanoparticle diameter can be controlled from 1.5 nm to 9.6 nm.     

Surface Trapping and STM Observation of Conformational Isomers of a Bis(Terpyridine) Ligand from Metallosupramolecular Grids

Tetranuclear Co‐grid complexes incorporating bis‐tridentate ligands, namely 4,6‐bis(2,2′‐bipyrid‐6‐yl)‐2‐phenylpyrimidine, were electrosprayed onto a Au(111) substrate under an ultrahigh vacuum. Fragmentation occurs leaving the ligands in four different conformations. Most ligands are found to form H‐bonded dimers. The most abundant conformer of the ligand on the Au surface is an asymmetric form, which has not been observed before. The present results indicate that the fragmentation of coordination compounds during the deposition process, in principle, allows for surface trapping, identification, and investigation of high energy, out‐of‐equilibrium conformations of the ligand molecules at low temperatures, which otherwise would not be observable.